A "Double Dividend", after all?

Transcription

1 A "Double Dvdend", after all? by K. J. Mun CES, Catolc Unversty of Leuven and EPRU, Insttute of Economcs, Unversty of Copenagen August, 999.

2 Abstract Te consensus vew among economsts seems to be tat a green tax reform s unlely to be assocated wt a "double dvdend" (Bovenberg 998). However, te results derved n te present paper suggest tat ts vew needs to be qualfed. We demonstrate tat a green tax reform s lely to be assocated wt a sgnfcant "double dvdend" f te government pror to tang te envronmental aspect nto account as adopted a proportonal tax structure due to te admnstratve costs nvolved n dfferentatng commodty tax rates, and f te green tax reform stmulates te labour supply and as desrable ncome dstrbutonal effects. Correspondance: Knud J. Mun, Center of Economc Studes, Katolee Unverstet Leuven Naamse straat 69, B-3 Leuven Pone Fax E-mal: Knud.Mun@econ.uleuven.ac.be Keywords: Optmal taxaton, externaltes, admnstratve costs, green tax reform, double dvdend JEL classfcaton codes: H, H9 Acnowledgements: Te wor for ts artcle as been made partly at CES, Catolc Unversty of Leuven, and partly at te EPRU, Insttute of Economcs, Unversty of Copenagen. Te resources provded at bot places for ts wor are gratefully acnowledged. Comments by Ken Tomson, Søren Bo Nelsen, Inger Mayeres, Gunnar Torlund Jepsen, Peter Brc Sørensen and partcpants at te 55t IIPF Congress n Moscow ave been very elpful..

3 Introducton Te "double dvdend" queston,.e. weter replacng a tax on labour wt taxes on commodtes causng envronmental damage wll ncrease socal welfare, not only by nternalsng te costs of te envronmental damage, but also by reducng te dstortonary costs of te tax system, as been consdered extensvely n te lterature. Based on te dea tat te tax revenue obtaned from envronmental taxes could be used to reduce pre-exstng dstortonary taxes, te frst contrbutons suggested tat a green tax reform n general would be assocated wt a "double dvdend". But after a number of publc fnance economsts, n partcular Bovenberg and s co-autors (Bovenberg and de Mooj 994a, 994b, Bovenberg and van der Ploeg 994a, 994b, 998a, 998b, Bovenberg and Goulder 997), ave extensvely consdered te queston, t as become clear tat te ntuton bend te ntal suggeston was flawed by not tang nto account te dsncentve effect of te envronmental taxes for te supply of prmary factors. Now, te consensus vew among economsts seems to be tat a green tax reform s unlely to generate a sgnfcant "double dvdend", f prevous polces ave been economcally ratonal. Te man motvaton for te present paper s to callenge ts vew. Frstly and fundamentally, by demonstratng tat te standard teoretcal publc fnance analyss by dsregardng te mportance of admnstratve costs for te optmal tax structure, unduly rules out te potental for a green tax reform to be assocated wt a "double dvdend". Secondly, by argung tat to be relevant n te context of actual polcy mang, as t was ntally ntended, te "double dvdend" concept sould be defned to reflect not only te cange n dstortonary costs of taxaton, but also te dstrbutonal consequences of a green tax reform. Te potental of a "double dvdend" does not depend on tang te dstrbutonal aspect nto account, and s n tself not suffcent for a "double dvdend" to materalse, but t ncreases consderably te number of cases were a green tax reform wll be assocated wt a "double dvdend". Goulder (995) defnes "te double dvdend" (n te context of te so-called "strong "double dvdend" proposton") as te negatve of te "reducton n ndvdual welfare, abstractng from te welfare effect from canges n envronmental qualty" assumng a revenue neutral substtuton of te envronmental tax wt "typcal or representatve dstortonary taxes". He justfes s defnton by te fact tat polcymaers wo are nterested n a green tax reform are often frustrated wt te complextes of evaluatng suc reforms. If a polcy-maer could assume tat te net benefts due to oter factors tan te drect envronmental effects and te admnstratve costs of regulaton were non-negatve, ten s tas would be reduced to argue tat te benefts due to tese drect effects were postve, and tus be consderably smplfed. Ts justfcaton suggests tat te tas of te decson-maer would be facltated by te dentfcaton of condtons wc, wen satsfed, would assure a postve net beneft of te tax canges not only due to reducton n te dstortonary costs of taxaton but also due to mprovement of te ncome dstrbuton. But altoug t s clear from Sandmo 975's semnal contrbuton to te analyss of te optmal taxaton and tax reform n te presence of externaltes tat dstrbutonal effects are mportant for te optmal soluton, ts aspect s not taen nto account n Goulder's defnton. In a contemporaneous contrbuton Proost and Van Regemorter

4 (995) ponted out te lmtaton of basng te defnton of te "double dvdend" on te effcency aspect only, and suggested a generalsaton of te concept to nclude also te dstrbutonal benefts of te tax canges. Neverteless t seems tat Goulder (995) n te economc lterature remans te standard reference wt respect to te defnton of te "double dvdend". Bovenberg (998) for example revews te "double dvdend" dscusson based on ts defnton. Welfare economc analyss of optmal taxaton and project evaluaton n te presence of externaltes s as oter areas of second best welfare economcs complex and te results not always ntutve. However, te understandng of te teoretcal results s often facltated by consderng an example wc, altoug llustratve, refer to a concrete real lfe stuaton. To support te nterpretaton of te teoretcal analyss we terefore provde a quanttatve analyss of wy a green tax reform, wc nvolves te ntroducton of a dfferentated tax on lesure travel, s lely to be assocated wt a sgnfcant "double dvdend". Te paper s organsed as follows: In Secton, we formulate matematcally te government's maxmsaton problem subject to condtons wc nclude restrctons on te set of feasble tax nstruments to reflect te admnstratve costs assocated wt ter use. In Secton 3, we defne te "te double dvdend" of a "green tax reform" and derve an approxmate crtera for te "double dvdend" to be postve. After avng brefly revewed relevant results of te teory of optmal taxaton, we dentfy condtons conducve to a green tax reform beng assocated wt a "double dvdend". In Secton 4, we support te nsgt ganed n te teoretcal analyss by smulaton results produced wt te elp of an llustratve CGE model, wc satsfy te condtons dentfed. A fnal secton summarses and concludes te paper suggestng promsng avenues for future researc. Te specfcaton of te CGE model and detals on te smulaton results are contaned n Annex. Te model We consder a closed economy operatng under condtons of perfect competton wt a large number of ouseolds, a large number of frms and a government. Te government aderes to egaltaran value judgements and maxmses socal welfare defned accordngly, subject to te constrants mposed by te structure of te economy. Te ouseolds ave dfferent sll levels, but supply only one omogeneous prmary factor, labour. Tey demand two produced commodtes, a drty good", wc s assocated wt external dseconomes, and a clean good", wc s not. We assume tat only te aggregate level of te consumpton of te "drty good" - not ts dstrbuton among ouseolds - matters. Te producton sde of te economy s represented by two constant returns to scale producton sectors, eac producng one output and usng only labour as nput. Government consumpton s exogenous, except for te costs assocated wt tax admnstraton. For te usual To facltate te exposton only two rater tan a greater number of produced commodtes are consdered. However, a notaton as been used to facltate te comparson wt te case of many commodtes as e.g. n Sandmo (975).

5 reasons (see Atnson and Stgltz 98, p357), we do not consder te optmal dfferentaton of lump-sum taxes among ouseolds as a realstc opton for te government. Based on smlar consderatons, but more unconventonally, we furtermore assume tat te admnstratve costs of tax admnstraton depend on te complexty of te tax structure, more specfcally tat a proportonal tax structure n te form of a proportonal ncome tax (wage tax) or a unform commodty tax, are te admnstratvely least costly tax systems, requrng te government to gater and process less nformaton tan n te case of alternatve tax systems. Wc tax system te government cooses, a wage tax, a VAT, a lnear ncome tax, or an ncome tax combned wt dfferentated commodty taxes, s tus not gven a pror, but depends on te admnstratve costs nvolved. Houseolds are labelled (,.,H) H, labour, te "drty good" and te "clean good" (,) C. Houseolds face consumer prces, q ( q, q,q ) and frms face producer prces p ( p, p,p ). We assume tat all ouseolds ave te same tme endowment, but dffer n productvty,.e. tat te net demand of labour for te t ouseold s x =- ψ ( ù c ), were ω s te tme endowment, c te consumpton of lesure, and ψ an ndex of labour productvty. Te t ouseold's net demand vector s denoted by x ( x,x ) and ts preferences are represented by u = u (,e) x x, were e represents te publc good externalty. Te correspondng ndrect utlty functon s expressed by v ( q, e, I ), were I represents unearned ncome. For eac ouseold ( q, e, u ) qx = E (, e, u ) q were ( q, e, u ) x s te vector of compensated demand functons and E ( q, e, u ), te expendture functon, wc ndcates te mnmum level of expendture at wc te utlty level u can be aceved at te ouseold prces q and at te level of te publc good externalty e. Te t ouseold's valuaton n monetary terms of a margnal ncrease n te E externalty s tus - E e - ( q, e, u ). We defne te followng terms to smplfy te notaton E E ( q, e, u ) = x ( q, e, u ), q Ej E E e q E q q j x j = ( q, e, u ) = ( q, e, u ) q E x = ( q, e, u) q E j H E j H X j - x H j E e - Ee H H H x x, x x q E and E j E j e E e H H 3

6 Te functonal relatonsp between te externalty and te aggregate consumpton of te "drty good", commodty, s represented by e = e x. H We assume a lnear producton structure and perfect competton. By te approprate coce of unts and by coosng labour as numerare, we can terefore wtout loss of generalty assume all producer prces to be equal to,.e. p = ( p p,p ) (,, )., = Te government's expendtures, A, are fnanced by commodty taxes, t q p, and a unform lump-sum tax, T. Tus, unearned ncome s for all ouseolds equal to te unform lump-sum tax,.e. I =-T. A(q,p) ndcate ow A depend on te tax structure; A(q,p) s omogeneous of degree zero n q, equal to A( p ) for t = t, and equal to A( p ) + A( p) for t t. 3 A( p) may terefore be nterpreted as te extra admnstratve costs of a dfferentated compared to a proportonal tax structure. Te government's preferences are expressed by an ndvdualstc, Pareto socal H W u,u,..,u. Usng te expendture functon approac (as for welfare functon W= ( ) example n Mun 978), we may terefore specfy te government's problem n terms H u = u,u,..,u 4, of te maxmsaton of socal welfare wt respect to T, q, e and ( ) subject to te followng constrants: ) E ( q, e, u ) = T, H, wc says tat te levels of ndvdual utlty must be consstent wt te level of unearned ncome,.e. = T. Tese constrants rule out ndvdualsed lump-sum transfers, but allow for a lnear ncome tax. I ) A( q, p) = t E ( q, e, u ) +HT, wc may be nterpreted as te = H government's budget constrant. Ts constrant represents te tree sets of general equlbrum condtons,.e. te condtons for proft maxmsaton, utlty maxmsaton and materal balance. T s negatve f t s nterpreted as te fxed element n a progressve lnear ncome tax scedule. 3 Te admnstratve costs of tax admnstraton consst of te costs of tax collecton and te costs of tax enforcement. Tey are terefore lely to depend on bot te complexty of te tax system and te level of te tax rates. We abstract, owever, for te sae of smplcty from te dependence of te admnstratve costs on te level of te tax rates, snce t s not relevant for ponts we are gong to mae n ts paper. 4 Only T and t are te polcy nstruments. Snce producer prces are fxed coosng consumer prces, q p + t, corresponds to coosng t. Te ouseold utltes, u, and te externalty, e, are ncluded n te set of controls to facltate te nterpretaton of te frst order condtons by provdng expressons for te easy dervaton of te net margnal socal welfare of ncome, µ, and for te socal value of a margnal ncrease n te externalty, ρ. 4

7 3) e = e E ( q, e, u ), wc represents te relaton between te level of H te publc good externalty and te levels of consumer prces and ndvdual utltes, and 4) q p = q p. Ts constrant represents te restrctons on te government's coce of commodty tax rates wen, compared to a proportonal tax structure, dfferentatng te commodty tax rates, te benefts n terms of lower dstortonary costs of taxaton and a more desrable ncome dstrbuton are smaller tan te extra admnstratve costs, A( p). To fnd te optmal tax structure te government terefore as to solve two maxmsaton problems. Te frst to maxmse socal welfare subject to te constrants -3, and te second subject to te constrants -4. Te optmal tax structure s ten tat of te two solutons wc s assocated wt te largest level of socal welfare. Te Lagrangan correspondng to te government's maxmsaton problem may, n te frst case were and A(q,p) = A( p ) + A( p), be wrtten as H L = W ( u,u,..,u ) µ ( T E ( q, e, u )) + H + λ t E ( q, e, u ) + HT A(q,p) = H + ( ) ρ e E e u e q,, H and n te second case were A(q,p) = A( p ), as L = L + γ ( ) q () q From te frst order condtons wt respect to u we ave () L u = W u -µ E u + λt = de E u + ρ E u = (3) and usng tat v E u =/ ( q, e, I ), x v E u = ( q, e, I ) / ( q, e, I ) we obtan µ = β + λ x de x t + ρ I = (4) W v were β s te margnal socal value of ncome for ouseold. We may u tus nterpret µ, n analogy wt Damond 975's net margnal socal value of 5

8 ncome for ouseold, as te ncrease n socal welfare f te ncome of te t ouseold were ncreased by one unt from outsde te economy. From te frst order condtons wt respect to e we ave L = - µ = H E e E e = H + λ de t + ρ E e ρ = (5) H Substtutng for - β = H E e µ we ave - λ t = H E e H E e x + de x E e E e H H ρ -ρ = (6) from wc we may obtan te followng expresson for te socal value of a margnal ncrease n te publc good externalty ρ = H β E e + λ = t de (7) Te frst element n te bracet, - H β Ee, s te socal value of a margnal ncrease n te externalty, dsregardng te adjustment n ouseold demand. Te second element, λt, s te opportunty cost value of te cange n tax revenue due to = cange n consumpton caused by a margnal ncrease n te externalty. Te last factor,, may be nterpreted as an adjustment, tang nto account te de effect on te demand for te "drty good" of te cange n te externalty, to te partal socal welfare effect of an ncrease n te externalty n order to get te total effect. From te frst order condtons wt respect to T we ave L T = - = H µ + λ H = ' (8) Substtutng for µ we ave wen a lnear ncome tax s feasble tat te opportunty cost prce of government funds s λ = β v + λt x = H (9) 6

9 Te remanng frst order condtons for a maxmum are L q L q L q = - µ = = H - H = - µ = H x x x + λ H + λ H + λ H x + λ E = H x + λ de t + ρ E = () = E H x + λ E = H H de t + γ + ρ E = () H de t - γ + ρ E = () H 3 Optmal tax structure and green tax reform 3. Te optmal tax structure. Crtera for desrable tax reforms are closely lned to te condtons for an optmal tax structure (see Dxt 975). As bacground for te subsequent analyss of condtons, wc guarantee a "double dvdend" of a green tax reform, we terefore brefly summarse te basc nsgt of optmal commodty tax analyss n te case were tere are no externaltes and no restrctons on te government's coce of commodty tax rates. In an economy wt only one representatve ouseold all commodtes must be dscouraged at te same rate (see Ramsey 97). In te case of only two produced commodtes, te commodty, wc s more complementary wt lesure and for wc an ncrease n te tax rate wll terefore provde a relatvely small encouragement to te consumpton of lesure, wll be taxed at a ger rate (see Corlett and Hague 953). In te specal and unrealstc case of lesure beng separable from consumpton, te optmal tax structure s proportonal (see Deaton 98). In an economy wt many ouseolds te dscouragement s, oter tngs beng equal, relatvely low for commodtes wt relatvely g ncome elastcty, and vce versa. Te actual tax structure depends, owever, f tax revenue s rased by an ncome tax crucally on ts caracterstcs. Wen te government's revenue requrement s fnanced by a lnear ncome tax, ten, general speang, normal goods wll be taxed wereas nferor goods wll be subsdsed. Wen te government's revenue requrement s fnanced by a proportonal ncome tax (.e. T constraned to be zero), ten, general speang, goods wt an ncome elastcty above wll be taxed, wereas not only nferor goods, but also normal goods wt an ncome-elastcty suffcently below (ow muc below wll depend on opportunty costs of government funds, λ ) wll be subsdsed (see Mun 977). 7

10 3. Green tax reform and te "double dvdend" Defntons sould be judged on weter tey are elpful or not n te context were tey are to be used. We assume, followng Goulder (995), tat te ultmate purpose of defnng te "double dvdend" s for te defnton to be useful n te context of provdng advce to polcy-maers wo consder mplementng a green tax reform,.e. n stuatons were a polcy-maer as become aware of some envronmental effects and s consderng weter t s wortwle to cange te tax structure to nternalse tese effects. An example s te realsaton by polcy-maers of te potental damage of CO polluton n te late 8es. It was n ts context tat te term te "double dvdend" was frst used by Pearce (99) n suggestng tat a tax on CO emsson would not only dscourage envronmental damage, but also produce a "double dvdend" by reducng te dstortonary costs of te tax system. We assume tat ouseold beavour before and after people ave become aware of te envronmental damage assocated wt te consumpton of te "drty good" s te same. We terefore represent te socal preference before te cange n awareness of te envronmental effects by ~ W ({ v ~ (, e, I ), H} ) = W q were v ~ = for all H (3) and (consstent wt te formulaton n Secton ) after by W= W ({ v (, e, I ), H} ) q were v < for all H (4) Based on tese socal welfare functons we ten defne a green tax reform ( t, T ), as te tax canges transformng te ntal tax structure, (t I, T I ), wc s optmal wen no value s attaced to te external effects,.e. wen based on ~ W = W v~ q, e, I, H, nto te tax structure, (t *, T * ), wc s optmal wen ({ ( ) }) envronmental damage s taen nto account,.e. wen based on W v q, e, I, H. ({ ( ) }) Te cange n socal welfare assocated wt te green tax reform may terefore be expressed as I I I I I ({ q }) - W ({ v (, e ( q, T ), T ), H} ) W W v ( *, e *( q*, T *), T *), H q (5) We dvde W nto two dvdends: te "frst dvdend", D, beng te cange n socal welfare due to te decrease n te externalty, I I I e e* ( q *, T *) - e ( q,t ), net of te ncrease n te admnstratve costs, A, f any 5 ; and te "second dvdend", D, beng te resdual cange n socal welfare due to canges n te dstortonary costs of taxaton and n te dstrbuton of ncome. Te dstncton s based on te 5 We assume A to be equal to zero f te tax rate of te "drty good" dffers from tat of te "clean good" already before te green tax reform. 8

11 assumpton tat te "frst dvdend" s relatve easy to estmate or at least to conceptualse, wereas te "second dvdend", especally for non-economsts, s muc more dffcult to evaluate. We defne a green tax reform to be assocated wt a "double dvdend" f te "second dvdend" s postve. Wen becomng aware of te mportance of envronmental effects, polcy-maers are often, as ponted out by Goulder (995), frustrated by te complextes of evaluatng green tax reforms due to te dffculty n evaluatng te "second dvdend". If a polcy-maer could assume tat te benefts due to oter factors tan te mprovement n envronmental qualty and te ncrease n te costs of regulaton were non-negatve, ten s tas would be muc smpler. In oter words, te dentfcaton of condtons wc would assure tat te green tax reform were assocated wt a "double dvdend", as defned ere, would potentally facltate te tas of te decson-maer consderably. Note tat, altoug motvated by te same general objectve, our defnton dffers from te one due to Goulder n tang te dstrbutonal aspect nto account 6. Te defnton s terefore, n our opnon, more relevant to polcy-maers, and also more consstent wt ter decson-mang process. Effcency gans cannot be separated from dstrbutonal gans wen cost-free ndvdualsed lump-sum transfers are not possble, wc n fact tey never are. Snce, as ponted out by Proost and Van Regemorter (995), and recognsed by Bovenberg (998), almost all governments beave as f tey were nequalty-averse - a defnton of te "double dvdend" wc does not tae ts nto account seems terefore, f properly understood by polcymaers, not to be pertnent, and, f not properly understood, potentally msleadng. A ratonal polcy-maer sould desgn a green tax reform tang nto account s dstrbutonal preferences. If e uses a defnton of te "double dvdend" based only on effcency consderatons, e may easly be msled to evaluate te effects of te tax canges as f e were nequalty-neutral, wc n general would be nconsstent wt s preferences. In order to dentfy condtons, wc wll assure a postve "double dvdend" t s elpful to consder a frst order approxmaton of te cange n socal welfare due to a green tax reform. We consder te case were before te green tax reform due to te admnstratve costs of dfferentated tax rates te commodtes are taxed at te same rate. A unform commodty tax s equvalent to a wage tax; we may terefore, wtout loss of generalty, assume tat, pror to reform, te commodty tax rates are zero,.e. t = for =,, and lmt ourselves to consder tax reforms were te labour tax rate reman constant,.e. t t I =. Te green tax reform releases te tax constrants, and tus ncreases te admnstratve costs by A. We also assume tat te ntal tax structure eter as been optmsed wt respect to te lump-sum tax, T, or tat T remans uncanged n real terms. In te case of a proportonal ncome tax te cange n tax revenue by ncreasng te tax on te "drty good" to nternalse te externalty s terefore balanced by cangng te tax rate on te "clean good", wereas n te case of a lnear ncome tax te green tax reform may also nvolve a cange n T. 6 It also dffers n assumng tat polcy-maers, nterested n ts type of measure, are ratonal. 9

12 Te cange n socal welfare due to a green tax reform may, gven tese assumptons, by propertes of Lagrangan multplers be approxmated by Wˆ γ t - t )- λ A (6) ( Te frst element on te rgt-and sde of te equalty sgn represents te beneft of dfferentatng te tax structure. Te second element s te opportunty cost value of te admnstratve costs assocated wt te dfferentated rater tan a unform commodty tax 7. From te frst order condtons for an optmal tax structure wt respect to q and q, () and ), we obtan te followng expresson for te opportunty costs value of te tax constrant: γ = λ t E + λ x - µ x + de ρ E H H = -( λ t E + λ x - µ x + de ρ E ) (7) H H Substtutng for γ, µ and ρ, and collectng terms we ave (see Tecncal Appendx) Wˆ = λt C q t + λt ê H β Ee ê + C ( λ - R )X t (8) were R H β X x s te dstrbutonal caracterstc of commodty, and de ê = de t te frst order approxmaton of te cange n te = q externalty due to te green tax reform. 3.3 Condtons conducve to a postve "double dvdend" Usng te framewor tus establsed, we n ts secton frst explan wy, as n te standard analyss of te "double dvdend" queston, gnorng te mportance of admnstratve costs for te optmal tax structure leads to te vew tat te "double dvdend" s always negatve. We ten brefly restate te case wy t s realstc to expect tat te tax structure pror to a green tax reform s restrcted by admnstratve costs, and based on ts assumpton move on to dentfy condtons under wc a green tax reform wll be assocated wt a "double dvdend". 7 Te crtera tus tae nto account tat te ncreased admnstratve costs wll ave to be fnanced by dstortonary taxaton.

13 It follows from a smple argument tat f te tax constrant s non-bndng before a green tax reform,.e. were te socal welfare functon attaces no value to te cange n te externalty, ten te "double dvdend" s non-postve. If te tax structure before te green tax reform s optmal gven te socal welfare functon, W v ~ q, e, I, H, ten te cange n socal welfare due to any feasble tax ({ ( ) }) reform, ncludng te green tax reform, ( t, T ), must by defnton be nonpostve,.e. W. However, W s wen te tax constrant s non-bndng equal ~ ~ W v q, e, I, H. A green tax to te second dvdend calculated based on ({ ( ) }) reform wll terefore, wen pror to reform te tax constrant s non-bndng, never be assocated wt a "double dvdend". Tere are two reasons wy te tax constrant may be non-bndng pror to a green tax reform. Frst, tat te optmal tax structure s proportonal, even dsregardng te costs of dfferentatng te tax structure. In an economy wt only one representatve consumer were consumpton s separable from lesure, as te one consdered n Bovenberg (998), ts s te case. In suc an economy, wen no value s attaced to te externalty, a proportonal tax structure s te optmal soluton to te government's maxmsaton problem. Terefore te tax constrant wll not be bndng. Replacng a wage tax by a unform commodty tax does not cange te allocaton, and dfferentatng te commodty tax structure to decrease te externalty wll n ts case dscourage te supply of labour and ence ncrease te dstortonary costs of taxaton. A green tax reform, wc replaces a wage-tax wt a dfferentated commodty tax structure to nternalse te externalty, wll terefore not be assocated wt a "double dvdend". Te second reason wy te tax constrant may not be bndng pror to a green tax reform, s tat t as been optmal to dfferentate te tax structure already before tang te envronmental aspect nto account,.e. tat te admnstratve costs needed to dfferentate te tax rates ave already been ncurred pror to te mplementaton of te green tax reform. However, n te context of provdng relevant polcy advce to conclude on ts bass tat a green tax reform wll never be assocated wt a "double dvdend", s clearly to go too far. To assume tat consumpton s separable from lesure s a very restrctve assumpton, and n a many ouseold economy far from suffcent for a proportonal tax structure to be optmal. Tere are n fact no convncng justfcaton for assumng tat a proportonal tax structure sould be optmal, oter tan te admnstratve costs for suc a tax structure are lower tan tose of a dfferentated tax structure. It terefore reasonable to expect tat pror to a green tax reform te admnstratve costs nvolved n dfferentatng commodty tax rates n many cases constran te tax structure to be proportonal. It s terefore relevant, accordng to te justfcaton provded above, n te context of defnng te "double dvdend", to try to dentfy condtons conducve to a green tax reform beng assocated wt a "double dvdend" based on ts assumpton. To do tat, we use te frst order approxmaton of te cange n socal welfare due to a green tax reform, derved n te prevous secton. Based on te defnton provded above, te "frst dvdend" of te green tax reform may be approxmated by ˆD - H β E e ê (9)

14 and te "second dvdend", terefore by ˆD Wˆ or by substtutng for -(- β H E e ê - Wˆ usng (6), by ˆD = ) γ( t - t + β H E e λ A ) () ê () and usng (8), by + C ˆD t λ ( E C ( λ - R )X t t + E e ê )+ λ t x ( H x t x + H I E e ê ) () Based on (), ˆD " may be dvded nto two elements, ˆD. and ˆD. : ) Te approxmaton of cange n socal welfare due to te cange n te dstortonary cost of taxaton, ˆD = t. λ ( E C t + E e ê )+ λ t x ( H x t x + H I E e ê ) (3) s te sum of two man effects, represented by te two bracets n (3). Te last bracet represents te ncome effect. Assumng tat lesure s a normal good ts effect wll tend to ave te same sgn as te cange n socal welfare and can terefore be dsregarded n determnng te sgn of te cange n socal welfare 8. Te sgn of te cange n socal welfare s tus n general determned by te frst bracet: te cange n tax revenue caused by te cange n te supply of te labour ) due to te nduced decrease n te externalty, E ê, and ) due to te cange n tax rates drectly, C labour,.e. f t E t t e. If te decrease n te externalty ncreases te supply of te eˆ e >, t contrbutes to an ncreased socal welfare; f te opposte s te case, t decreases socal welfare. Te drect effect of te cange n te tax rates on te labour supply, t E t, wll only be postve f te C consumpton of te "drty good" s complementary to lesure. In ts case a move from a proportonal tax structure to a tax structure n wc te "drty good" s taxed at a ger rate tan te "clean good", wll decrease te costs of taxaton and tus, ceters parbus, ncrease socal welfare. Ts s consstent wt te commodty, te consumpton of wc s more complementary wt lesure and for wc an ncrease n te optmal tax rate wll terefore provde a relatvely small encouragement to te consumpton of lesure, based on effcency consderatons alone wll be taxed at a ger rate (cf. Corlett and Hague 953). 8 Te effect wll strctly ave te same sgn as te cange n socal welfare n te case of a one ouseold economy suc as te one consdered n Bovenberg (998).

15 ) Te approxmaton of te cange n socal welfare due to ncome dstrbutonal effects (due to te canges n tax rates wtout tang te cange n te externalty nto account) ˆD. =( λ - R C )X t (4) wc s postve f te value of te tax payments valued by dstrbutonal caracterstcs s greater tan wen valued at te opportunty cost of government funds. Wen te government's revenue requrement s fnanced by a lnear ncome tax, we ave from te frst order condtons wt respect to T, (), tat λ =β v x + λt. If te "drty good" s a normal good, R < β v. Terefore f H H ˆD wll, n general, be te government can rase tax revenue by a lnear ncome tax,. postve f te ncome elastcty of te "drty good" s greater tan zero. If te government s constraned to rase ncome tax revenue by a proportonal ncome tax ˆD wll, n general, be postve f. R < R,.e. f te ncome elastcty of te "drty good" s greater tan one. To summarse, f te tax structure pror to te green tax reform as been proportonal due to admnstratve costs, ten te followng two condtons are suffcent for a green tax reform to be assocated wt a postve "double dvdend": Frst, tat te tax sft and te resultng cange n te externalty dscourage te consumpton of lesure. Ts wll be te case f te "drty good" and te externalty are complementary to lesure. Secondly, tat te tax sft mproves te dstrbuton of ncome (leavng asde te ncome dstrbutonal effects of te cange n te externalty). Generally speang, ts wll be more lely to be te case te more te "drty good" consumed by te "rc". Weter te tax sft wll mprove te dstrbuton of ncome or not depends crtcally on te type of ncome tax used, for example weter t s a wage tax or a lnear ncome tax. 4 A quanttatve llustraton To support te nsgt ganed n te teoretcal analyss we provde a quanttatve llustraton tang as an example a green tax reform to nternalse te externaltes assocated wt lesure travel. Te results are derved from an llustratve CGE model wc s documented n te Annex togeter wt te detals of te smulaton results. As seems reasonable n te case of lesure travel, we assume tat te sare of ncome spent on te "drty good",.e. lesure travel, for g ncome ouseolds s greater tan for low ncome ouseolds, and tat te tme spent consumng te "drty good", s relatvely more mportant tan for consumpton n general. We assume tat te ouseolds' evaluaton of te envronmental damage assocated wt te consumpton 3

16 of lesure travel s proportonal to ouseold ncome, and tat te externalty s separable from te consumpton of fnal commodtes and lesure. Te extra admnstratve costs of a dfferentated tax structure are assumed to be unts greater tan of a proportonal tax structure 9. Fnally, we assume tat te government s nequalty-averse, attacng te double value to an ncrease n te ncome of lowncome ouseolds compared to tat of g-ncome ouseolds. Te opportunty costs of government funds are.4 (.3. f te government s alternatvely assumed to be nequalty-neutral). Wen te externalty s not taen nto account, te admnstratve costs mae t unattractve to dfferentate te tax structure altoug ts would sgnfcantly reduce te dstortonary costs of tax collecton and ave postve ncome dstrbutonal effects, gven te parameter values wc ave been cosen (see Annex, Table 3, Column () and (3)). However, bot for an nequalty-neutral and an nequalty-averse government a dfferental tax on lesure travel becomes desrable wen te envronmental benefts are taen nto account (see Annex Table 3, Column (3) and (4)). Table. Te ntal tax structure constraned by admnstratve costs. Inequalty- neutral Inequalty- averse Frst dvdend, D, of wc Envronmental benefts Admnstratve costs -3-4 Second dvdend, D 33 Cange n socal welfare 9 Source: Illustratve CGE model, Annex, Table 3 Table. Te ntal tax structure not constraned by admnstratve costs. Inequalty- neutral Inequalty- averse Frst dvdend, D 33 3 Second dvdend, D -7-4 Cange n Socal welfare 6 6 Source: Illustratve CGE model, Annex, Table 3 Tables and report te smulaton results n terms of te cange n socal value broen down on te "frst dvdend" and te "second dvdend" assumng, respectvely, tat te ntal tax structure s constraned by admnstratve costs, and tat t s not. We see tat n te case were te green tax reform nvolves a cange n admnstratve costs (Table ), bot for an nequalty-neutral and an nequalty-averse government te "double dvdend" s sgnfcant compared to te envronmental benefts. Te "double dvdend" for an nequalty-averse government s at relatvely more mportant tan for an nequalty-neutral government were t s only 9 For reference te GNP s 6.67, ouseold consumpton of lesure travel, 5., of oter goods, 9. and government consumpton, ( see Annex, Table ) 4

17 33. Ts llustrates tat te scope for a sgnfcant "double dvdend" s larger wen te dstrbutonal aspect s taen nto account tan wen t s not. However n te case were tere are no admnstratve costs (Table ) tere are no "double dvdend". Te smulaton results tus also llustrate te crucal role played by te assumptons concernng admnstraton costs. It would be easy to provde an example were te "double dvdend" s postve for an nequalty-averse polcy-maer, but negatve f only te effcency gans are taen nto account. Te smulaton model may tus also llustrate te potental confuson wc defnng te "double dvdend", based only on te effect of te dstortonary costs of taxaton, may create. 5 Summary and concludng remars Wt respect to te lelood of a green tax reform generatng a sgnfcant "double dvdend", te analyss as confrmed te prevalng opnon among economsts to te extent tat tere s no presumpton, even tang admnstratve costs nto account, tat a sft from ndrect taxaton to drect taxaton wt te objectve of nternalsng envronmental externaltes, s lely, n general, to generate a "double dvdend". If te optmal tax structure as been dfferentated to explot te benefts n terms of reducton of dstortonary costs of taxaton and a more desrable ncome dstrbuton, te "double dvdend", as defned n ts paper (and n Goulder 995), wll be negatve. However, te analyss as also sown tat n tose cases were envronmental objectves, on te one and, and te objectves of a more desrable ncome dstrbuton and of reducng te dstortonary costs of taxaton, on te oter and, justfy tax canges gong n te same drecton, but were te benefts, based on te second set of objectves taen n solaton, are too small to justfy te admnstratve costs of a dfferentated tax structure, a sgnfcant "double dvdend" may be a realstc possblty. In practce, t s undoubtedly qute common pror to a green tax reform for "drty goods", for admnstratve reasons to be taxed at te same rate as a large number of "clean goods". Te results establsed n ts paper are terefore not only of teoretcal nterest, but also, n te context of decson-mang on envronmental polces, of consderable relevance n practce. Furtermore, te paper as demonstrated tat te "expendture functon approac" n te case of externaltes, as n oter areas of publc economcs, facltates te analyss of optmal taxaton and project evaluaton. Te presence of externaltes provdes a supplementary reason wy tang admnstratve costs nto account can sgnfcantly modfy te optmal tax structure and crtera for project evaluaton. We ave n ts paper focused on ow to ntegrate te admnstratve costs of alternatve regulatory regmes n te teoretcal analyss n te smplest way possble, and terefore ave delberately based te analyss on te well-nown standard model wt only one prmary factor. Te smple model prevents, owever, certan mportant ssues from beng consdered, suc as for example weter a desrable green tax reform n tang admnstratve costs of alternatve regulatory regmes and ncome dstrbutonal effects nto account s lely to create productve neffcency, and ow governments 5

18 sould provde support to allevate pan of structural adjustment to ndustres partcularly affected by envronmental polcy canges. However, tese ssues may be analysed extendng te framewor to represent more tan one prmary factor, and sectors wt decreasng returns to scale, (see Mun 98 and 998). Suc an extenson of te analyss seems of partcular nterest n te context of te ongong searc among economsts and poltcal decson-maers for ways to reform te taxtransfer system to provde ncome support and ncreased employment opportuntes for low-slled worers dsadvantaged by globalsaton and tecnologcal cange. References Atnson, A.B. and J. Stgltz (98), Lectures on Publc Economcs, McGraw-Hll Bovenberg, A.L. and R.A. de Mooj (994a), "Envronmental Leves and Dstortonary Taxaton", Amercan Economc Revew, 84(4), 85-9 (994b), "Envronmental Taxaton and Labour-Maret Dstortons", European Journal of Poltcal Economy, (4), Bovenberg, A.L. and F. van der Ploeg (994a), "Green Polces n a Small Open Economy", Scandnavan Journal of Economcs, 96, (994b), "Envronmental Polcy, Publc Fnance and Labour Maret n a Second-Best World", Journal of Publc Economcs, 55(3), (998a), "Consequences of Envronmental Tax Reform for Involuntary Unemployment and Welfare", Envronmental and Resource Economcs (fortcomng) (998b), "Tax reform, Structural Unemployment, and te Envronment", Scandnavan Journal of Economcs, (fortcomng) Bovenberg, A.L. and L.H. Goulder (997), "Cost of Envronmentally Motvated Taxes n te Presence of Oter Taxes: General Equlbrum Analyss", Natonal Tax Journal, 5(), Bovenberg, A.L. (998), "Green tax Reform: Implcatons for Welfare and Dstrbuton", Paper presented at 54 t IIPF Congress, Cordoba, Argentna, -9 Goulder, L.H. (995), "Envronmental Taxaton and te "Double Dvdend": A Readers Gude", Internatonal Tax and Publc Fnance,, Corlett, W.J. and D.C. Hague (953), Complementarty and excess burden of taxaton, Revew of Economc Studes,, -3 Deaton, A.S. (98), "Optmal taxes and te structure of preferences", Econometrca, 9,

19 Damond, P.A. and McFadden, D.L (974), Some Uses of te Expendture Functon n Publc Fnance, Journal of Publc Economcs, 3, 3- Damond, P.A. (975), A many-person Ramsey Rule, Journal of Publc Economcs, 4, 7-44 Dxt, A. (975), Welfare Effects of Tax and Prce Canges, Journal of Publc Economcs, 4, 3-3 Mrrlees, J.A (976), Optmal tax teory. A syntess, Journal of Publc Economcs, 6, Mun, K.J., (977), Optmal Publc Sector Prcng Tang te Dstrbutonal Aspect Quarterly Journal of Economcs, Vol. LXXXXI, No. 4, (978) "Optmal Taxaton and Pure Proft", Scandnavan Journal of Economcs, 8, -9 (98), Optmal taxaton wt some non-taxable commodtes, Revew of Economc Studes, 47, (998), Sould governments create producton neffcency?, EPRU dscusson paper Perron, C. and T. F. Ruterford (995), "Regular Flexblty of Nested CES Functons", European Economc Revew 39, Proost, S. and D. Van Regemorter (995) "Te Double Dvdend and te Role of Inequalty Averson and Macroeconomc Regmes", Internatonal Tax and Publc Fnance,, 7-9 Ramsey, F.P. (97) " A contrbuton to te teory of taxaton", Economc Journal, 37, 47-6 Ruterford, T. (994), "Appled General Equlbrum Modellng wt MPSGE as a GAMS subsystem", Memo Sandmo, A. (975) "Optmal Taxaton n te Presence of Externaltes", Sweds Journal of Economcs, 77, Snow, A. and R.S. Warren (996), Te margnal cost of publc funds, Journal of Publc Economcs, 6,

20 Tecncal Appendx: Dervaton of approxmaton of cange n welfare due to green tax reform Substtutng for γ n (6) we ave Wˆ = C ( λ t E + λ H x - H µ x ) t + C ρ de E t - λ A Substtutng for µ Wˆ = λt +( C λ H = β C + λ ( E H x de x t + ρ I = dt - x - β x ) H x x ) t - λ A we get de x ( x ) I t + ρ E C H t and tus Wˆ = λt C q de t + ρ C q t +. C ( λ x - β x ) H H t - λ A Wrtng Rj H β X j x j and ê de de = q t, and usng tat ρ = β Ee + λt we get te followng approxmaton of H = de cange n welfare due to a green tax reform Wˆ = λt C q t + λt ê H β Ee ê + C ( λ - R )X t

21 Annex : Illustratve CGE model Introducton In ts note we document a CGE model, wc as been specfed to satsfy te condtons for te "double dvdend" to be postve, and report smulaton results to llustrate tat a green tax reform may generate a sgnfcant double dvdend, even f te government polces pror to tang te envronmental aspect nto account ave been economcally ratonal. Te CGE model as a number of caracterstcs wc, n our opnon, are essental n order for a CGE model to be used to address te ssues of a green tax reform n a poltcally relevant way. Toug smple, te CGE model provdes a flexble representaton of te nteracton between te consumpton and lesure for te varous commodtes. It allows te dfferences n admnstratve costs of dfferent regulatory regmes to be taen nto account, as well as te dstrbutonal consequences of tax canges by representng te ouseold sector by two types of ouseolds, a low-slled ouseolds and a g-slled ouseold, were te government attaces ger socal welfare wegts to te ncome of te former tan of te latter. Specfcaton of te CGE model For optmal tax analyses, te most mportant aspect of constructng a CGE model s n general te specfcaton of ouseold preferences. Often CGE models are based on assumptons tat mae tem unsuted for optmal tax analyses. Often an economy wt only one type of ouseold s consdered, and labour supply s assumed eter to be fxed, or, f endogenous, preferences are assumed to be omotetc wt te consumpton of produced goods beng separable from te consumpton of lesure. Tese assumptons mply, as we ave seen (Secton 3.), tat a proportonal tax structure s optmal. Tere are no compellng evdence for justfyng tese assumptons, rater te contrary ( see for example Myles 995). Tey may facltate te teoretcal analyss and model constructon consderably, and for some purposes tey may represent a justfable smplfcaton of realty. However, ts s seldom te case n second-best welfare economc analyses were tey may ndeed lead to conclusons wc n a practcal poltcal context are grossly msleadng wt respect to wat consttutes te optmal tax structure and desrable drectons of polcy reform. Te analyss of green polcy reform s by no means an excepton n ts respect. Te metodology poneered by Perron and Ruterford (995) and te correspondng computatonal tecnque (Ruterford 994) wc ave been adopted ere to specfy ouseold preferences avod te ptfalls of mang suc assumptons. Te followng supplementary assumptons ave been made to specfy te CGE model:

22 Te ouseold utlty functons, u ( x,e) u = U, are assumed to tae te form. C.. C.. L. ( C ( C ( x, c ; σ ), C ( x, c ; σ ), c σ ) + E e ; were c. s te tme used for te consumpton of commodty, and c. ndcates pure lesure,.e. te amount of tme spent on actvtes wc do not nvolve te L. consumpton of purcased commodtes. Te elastcty, σ, expresses for eac ouseold te substtuton between aggregate consumpton C and pure lesure c., D. σ s te elastcty of substtuton between te two composte goods e C and C, C. and σ te elastcty of substtuton between te amount purcased of te commodty, x, and te tme spent on ts consumpton c.... z = ω c c terefore s te tme spent supplyng labour to te maret. Te supply of labour n effcency unts (measured negatvely) s x = ψ z, were ψ s an ndcator of labour productvty. Te budget constrant for te t ouseold may terefore be expressed alternatvely as q x = Y, were q = ψ q s te ourly after-tax wage rate and COM = q z I s ouseold ncome. Ts specfcaton allows Y + ouseold preferences defned over mareted commodtes and labour, u (,e) x, to represent dfferent degrees of complementarty of te two purcased commodtes.. wt "lesure" n te sense of non-maret spendng of tme,.e. c = c + c. Te real ncome, bencmar stuaton, RI, of te t ouseold s defned to be equal to ts ncome n te C C. Y, plus te equvalent varaton of te polcy cange,.e.. RI = Y + E (, e, v ( q, e, I )) q - I In te case of an nequalty-adverse government, te socal welfare wegt assgned to te real ncome of te low-slled ouseolds s twce tat of te g-slled ouseolds. Assumng tat te number of low-slled and g-slled ouseolds are te same, te crtera for polcy cange to be desrable for an nequalty-neutral government s terefore tat W= LS RI + HS RI, and for an nequalty-adverse government tat W= LS RI + HS RI.. Note tat ts utlty functon s a specal case of te utlty functon defned on maret transactons, ( x e) u,, on wc te teoretcal analyss s based. Te results generated by te CGE model are terefore by assumpton consstent wt any result derved from te teoretcal model. Te externalty as been assumed to be addtvely separable wt a constant margnal utlty. Ts assumpton s not realstc, but tat s of lttle mportance for te ponts we want to llustrate ere.

23 Te bencmar data set on wc te CGE model s calbrated s provded n te form of a Socal Accountancy Matrx (SAM) (see Table ). Te functonal form for ow te externalty s related to te ouseolds' consumpton of te "drty good", commodty, s e = x HOUSE Table Te state of te economy pror to te green tax reform n te form of a SAM Total S S LS HS. Producton accounts for S eac sector S Materal balance accounts for eac commodty Commodty tax accounts for eac commodty 4. Materal balance account for labour Houseold ncome - LS expendture accounts HS Government budget account Total Note: S and S ndcate producton sectors, and, "drty good" and "clean good" respectvely, and LS and HS te low-slled and g-slled ouseold's, respectvely Te SAM represents 6 types of accounts, n total accounts as ndcated n Table. Note tat te sare of consumpton of te drty good, α, s % for te low-slled ouseolds, but 5% for te g-slled ouseold and tat te governments revenue requrement s fnanced by a 4% ncome tax, wc s equvalent to a 66 /3% unform tax on te consumpton of te produced commodtes. Te parameters of te utlty functons are provded n Table. For bot ouseolds te sares of tme spent consumng te "drty good", and te "clean good" relatve to.. ter sare of maret purcases, ( c / ω ) / α and ( c / ω ) / α, are specfed so tat te consumpton of te "drty good" requres relatvely more tme for ts consumpton tan te "clean good", and s terefore more complementary wt lesure. 3

24 Table Parameters Lowslled Hgslled L. σ.5.5 D. σ.5.5 C. σ.. ( α. c / ω) /.5.5. c / ω ).. ( α / Te CGE model as been specfed to generate llustratve results, rater tan to be realstc. Elastctes of substtuton between lesure and consumpton, wc determned te costs of government funds are.4, wc are n lne wt tose used n emprcal models (see Snow and Warren 996). Te model as been programmed n GAMS/MPSGE (see Ruterford 994). Te program can be obtaned from te autor. Smulaton results Te optmal tax structure as been calculated under four dfferent sets of assumptons. Te smulaton results n terms of ouseold taxes, government expendtures, supply of labour, te sze of te externalty and normatve ndcators (real ncome and socal welfare) are provded n Table 3. Te ntal state of te economy, were te government's tax revenue s rased by a proportonal tax structure (wage tax), s represented n Column. Columns and 3 represent wat would be te optmal soluton f te admnstratve costs of dfferentatng te tax rates between lesure travel and oter goods were taen as exogenous, wen, as as been assumed to be te case before te green tax reform, te government attac no value to te reducton n te externalty, assumng, respectvely tat te government s eter nequaltyneutral or nequalty-averse. Columns 4 and 5 represent te optmal solutons after te green tax reform under tese two alternatve assumptons. We see tat wen te admnstratve costs of dfferentatng te tax rates between te "drty good" and te "clean good" are taen nto account, ten a proportonal tax structure, as s n te ntal state of te economy, s te optmal soluton: dfferentatng te tax rates would wen te government s nequalty-neutral decrease socal welfare by 8 (see Columns ), and wen te government s nequalty-averse by 4 (see Columns 3). In contrast, a green tax reform wll f te government s nequalty-neutral ncrease socal welfare by 9, and under te alternatve assumpton tat t s nequalty-averse, by. 4

25 Table 3. Consequences of canges n polces State of te economy before te green tax reform Optmal tax structure wtout tang te externalty nto account Optmal tax structure tang te externalty nto account Houseold taxes () % Neutral() % Averse(3) % Neutral(4) % Adverse(5) % Labour, t Lesure travel, t Oter goods, t Level values Cange () -() Cange () -(3) Cange () -(4) Cange () -(5) Government expendtures Adm. costs and oter gov. exp Opportunty cost value Supply of labour and externalty Labour X Externalty e Value of reducton n externalty Normatve ndcators attacng no value to te externalty Dsregardng te externalty Tang externalty nto account Real ncome low-slled Real ncome g-slled Socal welfare Normatve ndcators attacng value to te externalty Dsregardng te externalty Tang externalty nto account Real ncome low-slled Real ncome g-slled Socal welfare Assumng tat te admnstratve costs are exogenous 5